Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equations
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AbstractIn this paper, we present a discontinuous Galerkin method with staggered hybridization to discretize a class of nonlinear Stokes equations in two dimensions. The utilization of staggered hybridization is new and this approach combines the features of traditional hybridization method and staggered discontinuous Galerkin method. The main idea of our method is to use hybrid variables to impose the staggered continuity conditions instead of enforcing them in the approximation space. Therefore, our method enjoys some distinctive advantages, including mass conservation, optimal convergence and preservation of symmetry of the stress tensor. We will also show that, one can obtain superconvergent and strongly divergence-free velocity by applying a local postprocessing technique on the approximate solution. We will analyze the stability and derive a priori error estimates of the proposed scheme. The resulting nonlinear system is solved by using the Newton's method, and some numerical results will be demonstrated to confirm the theoretical rates of convergence and superconvergence.
All Author(s) ListJie Du, Eric T. Chung, Ming Fai Lam, Xiao-Ping Wang
Journal nameJournal of Scientific Computing
Volume Number76
Issue Number3
PublisherSpringer Verlag
Pages1547 - 1577
LanguagesEnglish-United States

Last updated on 2020-31-07 at 23:14